Simple Equation With Two Values

[OneAndOne]

Hi. What's the correct symbol for the following values:

Any number greater than but not equal to zero to positive infinity. (any positive number not including zero)
Any number less than but not equal to zero to negative infinity. (any negative number not including zero)

Further, what equation could be written to express that all these positive and negative values are opposites and when added together will equal zero?

Sorry. I know this is really basic and should be easy to figure out. I just don't know the proper way to express this in an equation with the right symbols.

Thanks for your help!

 

[Deleted member 4993]

Hi. What's the correct symbol for the following values:

1)Any number greater than but not equal to zero to positive infinity. (any positive number not including zero)
2)Any number less than but not equal to zero to negative infinity. (any negative number not including zero)

Further, what equation could be written to express that all these positive and negative values are opposites and when added together will equal zero?

Sorry. I know this is really basic and should be easy to figure out. I just don't know the proper way to express this in an equation with the right symbols.

Thanks for your help!

Depends on type of class you are taking. In engineering (or in basic algebra), we would express those as:

1) 0 < x ≤ ∞

2)-∞ ≤ x < 0

The third question does not make sense to me!

 

[HallsofIvy]

Hi. What's the correct symbol for the following values:

Any number greater than but not equal to zero to positive infinity. (any positive number not including zero)

\(\displaystyle 0< x< \infty\) or, in "interval notation", \(\displaystyle x\in (0, \infty)\)

Any number less than but not equal to zero to negative infinity. (any negative number not including zero)

\(\displaystyle -\infty< x< 0\) or, in "interval notation" \(\displaystyle x\in (-\infty, 0)\)

Further, what equation could be written to express that all these positive and negative values are opposites and when added together will equal zero?

x+ (-x)= 0? I'm not clear what you mean by "all these positive and negative values". An individual positive number, added to its negative, is 0. But what you write could be interpreted as saying any positive number added to any negative number would equal zero, which is, of course, not true. Or it might be interpreted as a sum of all positive and negative numbers which does not even exist.

Sorry. I know this is really basic and should be easy to figure out. I just don't know the proper way to express this in an equation with the right symbols.

Thanks for your help!

 

[OneAndOne]

Depends on type of class you are taking. In engineering (or in basic algebra), we would express those as:

1) 0 < x ≤ ∞

2)-∞ ≤ x < 0

The third question does not make sense to me!

I understand your equation. And it truly does represent what I intended. I'm sure there are other ways to write it as well.

My third question is to simply show that all possible numbers on either side of 0 in the number system have opposites to infinity. And that when these opposites are added together they are equal to 0. For instance:

(-0.1) + (+0.1) = 0; (-1) + (+1) = 0; (-1,000,000) + (+1,000,000) = 0; (-∞) + (+∞) = 0;

Using your two equations I think it would look something like: (0 < x ≤ ∞) = (-∞ ≤ y < 0)

The only problem is that it doesn't show that x and y are exact opposites. How could I write the above and include the fact that x and y are opposites, meaning one x is a positive value that is the opposite of y which is a negative value?

Do you see a way to write this? Or does anyone see another way to write this that might be more suitable?

Thanks for your help! Your answer was good

 

[OneAndOne]

\(\displaystyle 0< x< \infty\) or, in "interval notation", \(\displaystyle x\in (0, \infty)\)


\(\displaystyle -\infty< x< 0\) or, in "interval notation" \(\displaystyle x\in (-\infty, 0)\)


x+ (-x)= 0? I'm not clear what you mean by "all these positive and negative values". An individual positive number, added to its negative, is 0. But what you write could be interpreted as saying any positive number added to any negative number would equal zero, which is, of course, not true. Or it might be interpreted as a sum of all positive and negative numbers which does not even exist.

Hey, that's a great answer! X + (-X) = 0 is really close to what I'm saying!

Only I want to say: x + (-x) = 0 where x is equal to every possible number in a series to infinity. How can i write this? We're so close! Is there way to express x as being a series of every number other than 0 to infinity?

Thanks so much for your help!

 

[mackdaddy]

(1+2+3...+infinity) + [-1+(-2)+(-3)...+(-infinity)]=0

what about that

 

[mackdaddy]

Actually it really should be (1+2+3...+|n|) + [-1+(-2)+(-3)...+(-|n|)]=0

 

[HallsofIvy]

Except that those are not true- you cannot treat divergent series like numbers.

OneandOne, first, do you mean something like "for all x, x+ (-x)= 0"?